给你出道题---最佳组合问题

Posted 2021-02-13 weiyinfu

给定N组数字，每组数字组内数字之间互不相同，组间数字可能相同。这些数字都是正整数，现在从这N组数字中选择尽量多的数字，是的选出来的数字满足以下条件：

• 每组只选出一个数字
• 选出来的数字互不相同

要求：使选出来的数字之和尽量大。

暴力想法显而易见，但是有没有更完美的方法呢？

import numpy as np


def generate_problem():
    group_count = np.random.randint(5, 6)
    groups = []
    for i in range(group_count):
        group_size = np.random.randint(2, 5)
        groups.append(sorted(list(set(np.random.randint(1, 10, group_size))), reverse=True))
    return groups


def brute_force(groups):
    groups = [i for i in groups if i]
    if not groups:
        return 0
    max_value = max(i[0] for i in groups)
    big_groups = [i for i in groups if i[0] == max_value]
    ans = 0
    for big in big_groups:
        next_groups = [j[1:] if j[0] == max_value else j for j in groups if j != big]
        s = brute_force(next_groups) + max_value
        ans = max(ans, s)
    return ans


def main():
    for i in range(100):
        p = generate_problem()
        s = brute_force(p)
        print(p)
        print(s)
        print('=' * 10)


main()